Finding closest object to CGPoint

Question

I have four UIViews on a UIScrollView (screen divided into quartiles)

On the quartiles, I have a few objects (UIImageViews), on each quartile.

When the user taps the screen, I want to find the closest object to the given CGPoint?

Any ideas?

I have the CGPoint and frame (CGRect) of the objects within each quartile.

UPDATE:

_{(source: skitch.com)}

Red Pins are UIImageViews.

    // UIScrollView
    NSLog(@" UIScrollView: %@", self);

    // Here's the tap on the Window in UIScrollView's coordinates
    NSLog(@"TapPoint: %3.2f, %3.2f", tapLocation.x, tapLocation.y);

    // Find Distance between tap and objects
    NSArray *arrayOfCGRrectObjects = [self subviews];
    NSEnumerator *enumerator = [arrayOfCGRrectObjects objectEnumerator];

    for (UIView *tilesOnScrollView in enumerator) {

        // each tile may have 0 or more images
        for ( UIView *subview in tilesOnScrollView.subviews ) {

            // Is this an UIImageView?
            if ( [NSStringFromClass([subview class]) isEqualToString:@"UIImageView"]) {

                // Yes, here are the UIImageView details (subView)
                NSLog(@"%@", subview);

                // Convert CGPoint of UIImageView to CGPoint of UIScrollView for comparison...
                // First, Convert CGPoint from UIScrollView to UIImageView's coordinate system for reference
                CGPoint found =  [subview convertPoint:tapLocation fromView:self];
                NSLog(@"Converted Point from ScrollView: %3.2f, %3.2f", found.x, found.y);

                // Second, Convert CGPoint from UIScrollView to Window's coordinate system for reference
                found =  [subview convertPoint:subview.frame.origin toView:nil];
                NSLog(@"Converted Point in Window: %3.2f, %3.2f", found.x, found.y);

                // Finally, use the object's CGPoint in UIScrollView's coordinates for comparison
                found =  [subview convertPoint:subview.frame.origin toView:self]; // self is UIScrollView (see above)
                NSLog(@"Converted Point: %3.2f, %3.2f", found.x, found.y);

                // Determine tap CGPoint in UIImageView's coordinate system
                CGPoint localPoint = [touch locationInView:subview];
                NSLog(@"LocateInView: %3.2f, %3.2f",localPoint.x, localPoint.y );

               //Kalle's code
                    CGRect newRect = CGRectMake(found.x, found.y, 32, 39);
                    NSLog(@"Kalle's Distance: %3.2f",[self distanceBetweenRect:newRect andPoint:tapLocation]);

            }

Debug Console

Here's the problem. Each Tile is 256x256. The first UIImageView's CGPoint converted to the UIScrollView's coordinate system (53.25, 399.36) should be dead on with the tapPoint (30,331). Why the difference?? The other point to the right of the tapped point is calculating closer (distance wise)??

<CALayer: 0x706a690>>
[207] TapPoint: 30.00, 331.00
[207] <UIImageView: 0x7073db0; frame = (26.624 71.68; 32 39); opaque = NO; userInteractionEnabled = NO; tag = 55; layer = <CALayer: 0x70747d0>>
[207] Converted Point from ScrollView: 3.38, 3.32
[207] Converted Point in Window: 53.25, 463.36
[207] Converted Point: 53.25, 399.36 *** Looks way off!
[207] LocateInView: 3.38, 3.32
[207] Kalle's Distance: 72.20 **** THIS IS THE TAPPED POINT
[207] <UIImageView: 0x7074fb0; frame = (41.984 43.008; 32 39); opaque = NO; userInteractionEnabled = NO; tag = 55; layer = <CALayer: 0x7074fe0>>
[207] Converted Point from ScrollView: -11.98, 31.99
[207] Converted Point in Window: 83.97, 406.02
[207] Converted Point: 83.97, 342.02
[207] LocateInView: -11.98, 31.99
207] Kalle's Distance: 55.08 ***** BUT THIS ONE's CLOSER??????

Answer 1

The following method should do the trick. If you spot anything weird in it feel free to point it out.

- (CGFloat)distanceBetweenRect:(CGRect)rect andPoint:(CGPoint)point
{
    // first of all, we check if point is inside rect. If it is, distance is zero
    if (CGRectContainsPoint(rect, point)) return 0.f;

    // next we see which point in rect is closest to point
    CGPoint closest = rect.origin;
    if (rect.origin.x + rect.size.width < point.x)
        closest.x += rect.size.width; // point is far right of us
    else if (point.x > rect.origin.x) 
        closest.x = point.x; // point above or below us
    if (rect.origin.y + rect.size.height < point.y) 
        closest.y += rect.size.height; // point is far below us
    else if (point.y > rect.origin.y)
        closest.y = point.y; // point is straight left or right

    // we've got a closest point; now pythagorean theorem
    // distance^2 = [closest.x,y - closest.x,point.y]^2 + [closest.x,point.y - point.x,y]^2
    // i.e. [closest.y-point.y]^2 + [closest.x-point.x]^2
    CGFloat a = powf(closest.y-point.y, 2.f);
    CGFloat b = powf(closest.x-point.x, 2.f);
    return sqrtf(a + b);
}

Example output:

CGPoint p = CGPointMake(12,12);

CGRect a = CGRectMake(5,5,10,10);
CGRect b = CGRectMake(13,11,10,10);
CGRect c = CGRectMake(50,1,10,10);
NSLog(@"distance p->a: %f", [self distanceBetweenRect:a andPoint:p]);
// 2010-08-24 13:36:39.506 app[4388:207] distance p->a: 0.000000
NSLog(@"distance p->b: %f", [self distanceBetweenRect:b andPoint:p]);
// 2010-08-24 13:38:03.149 app[4388:207] distance p->b: 1.000000
NSLog(@"distance p->c: %f", [self distanceBetweenRect:c andPoint:p]);
// 2010-08-24 13:39:52.148 app[4388:207] distance p->c: 38.013157

There might be more optimized versions out there, so might be worth digging more.

The following method determines the distance between two CGPoints.

- (CGFloat)distanceBetweenPoint:(CGPoint)a andPoint:(CGPoint)b
{
    CGFloat a2 = powf(a.x-b.x, 2.f);
    CGFloat b2 = powf(a.y-b.y, 2.f);
    return sqrtf(a2 + b2)
}

Update: removed fabsf(); -x^2 is the same as x^2, so it's unnecessary.

Update 2: added distanceBetweenPoint:andPoint: method too, for completeness.

Answer 2

If you're using Swift, here's how you can calculate the distance between a CGPoint and a CGRect (e.g. an UIView's frame)

private func distanceToRect(rect: CGRect, fromPoint point: CGPoint) -> CGFloat {
    // if it's on the left then (rect.minX - point.x) > 0 and (point.x - rect.maxX) < 0
    // if it's on the right then (rect.minX - point.x) < 0 and (point.x - rect.maxX) > 0
    // if it's inside the rect then both of them < 0. 
    let dx = max(rect.minX - point.x, point.x - rect.maxX, 0)
    // same as dx
    let dy = max(rect.minY - point.y, point.y - rect.maxY, 0)
    // if one of them == 0 then the distance is the other one.
    if dx * dy == 0 {
        return max(dx, dy)
    } else {
        // both are > 0 then the distance is the hypotenuse
        return hypot(dx, dy)
    }
}

Answer 3

Thanks @cristian,

Here's Objective-C version of your answer

- (CGFloat)distanceToRect:(CGRect)rect fromPoint:(CGPoint)point
{
    CGFloat dx = MAX(0, MAX(CGRectGetMinX(rect) - point.x, point.x - CGRectGetMaxX(rect)));
    CGFloat dy = MAX(0, MAX(CGRectGetMinY(rect) - point.y, point.y - CGRectGetMaxY(rect)));

    if (dx * dy == 0)
    {
        return MAX(dx, dy);
    }
    else
    {
        return hypot(dx, dy);
    }
}

Answer 4

Shorter @cristian answer:

func distance(from rect: CGRect, to point: CGPoint) -> CGFloat {
  let dx = max(rect.minX - point.x, point.x - rect.maxX, 0)
  let dy = max(rect.minY - point.y, point.y - rect.maxY, 0)
  return dx * dy == 0 ? max(dx, dy) : hypot(dx, dy)
}

Personally, I would implement this as a CGPoint extension:

extension CGPoint {
    func distance(from rect: CGRect) -> CGFloat {
        let dx = max(rect.minX - x, x - rect.maxX, 0)
        let dy = max(rect.minY - y, y - rect.maxY, 0)
        return dx * dy == 0 ? max(dx, dy) : hypot(dx, dy)
    }
}

Alternatively, you can also implement it as a CGRect extension:

extension CGRect {
    func distance(from point: CGPoint) -> CGFloat {
        let dx = max(minX - point.x, point.x - maxX, 0)
        let dy = max(minY - point.y, point.y - maxY, 0)
        return dx * dy == 0 ? max(dx, dy) : hypot(dx, dy)
    }
}